Grasshopper problem yields insight into quantum theory

December 4, 2017 by Lisa Zyga feature

 (Phys.org)—Like many mathematical puzzles, the grasshopper problem is simple to state but difficult to solve: A grasshopper lands at a random point on a lawn of area 1, then jumps once, a fixed distance, in a random direction. What shape should the lawn be in order to maximize the chance that the grasshopper stays on the lawn after jumping?

A first impression may be that the lawn should be in the shape of a circle, at least when the distance the grasshopper jumps is small. However, Olga Goulko and Adrian Kent, the two physicists who introduced the grasshopper problem in a new paper, have mathematically proved that a disc-shaped lawn is not optimal for any distance.

Instead, they discovered through numerical simulations that the optimal lawn shape takes on a variety of complex shapes for different jumping distances, such as a cogwheel shape for distances smaller than 1/π1/2(the radius of a circle of area 1, or approximately 0.56), while for larger distances, the optimal lawn consists of disconnected pieces. Often, but not always, these optimal shapes possess some type of symmetry.

Motivated by physics

Aside from being an interesting geometry problem, the grasshopper problem is also closely related to research in quantum physics and may have a variety of technological applications. In particular, the grasshopper problem is connected to the Bell inequalities, which famously show that, unlike classical physics models, quantum theory does not obey local realism. A prime example of the violation of local realism is seen in quantum entanglement, in which two distant entangled systems exhibit correlations that cannot be explained by any model that obeys local realism.

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Sound of crickets 'could become a thing of the past'

By Helen Briggs BBC News

10 February 2017

The first comprehensive assessment of Europe's crickets and grasshoppers has found that more than a quarter of species are being driven to extinction.

According to the International Union for Conservation of Nature (IUCN), the insect group is the most threatened of those assessed so far in Europe. 

Europe harbours more than 1,000 species of grasshopper and cricket. 

If we don't act now the sound of crickets could become a thing of the past, said the IUCN.

Crickets, bush crickets and grasshoppers - a group known as Orthoptera - live on grassland.

They are an important food source for birds and reptiles, and their decline could affect entire ecosystems. 

Their habitat is being lost due to wildfires, intensive agriculture and tourism development.

Jean-Christophe Vié, deputy director, IUCN Global Species Programme, said to bring these species back from the brink of extinction, more needs to be done to protect and restore their habitats.

"This can be done through sustainable grassland management using traditional agricultural practices, for example," he said. 

"If we do not act now, the sound of crickets in European grasslands could soon become a thing of the past."

The assessment took place over two years and involved more than 150 scientists.

Axel Hochkirch is chair of the IUCN invertebrate conservation sub-committee and lead author of the report.

Continued 

Frogs and grasshoppers: Why do legendary leapers have different ‘spring’ stiffness? – via Herp Digest

Date: September 16, 2016

Source: Brown University

New research on grasshoppers and bullfrogs offers a conclusion about jumping: When an animal has less time to store energy for a jump, it needs a less stiff tendon than one that can take its time.

A new research paper tells a story of the grasshopper and the bullfrog, but it's no children's tale. Instead, it describes biomechanical simulations that help to explain why the two jumping animals have very different stiffnesses in the springs -- tendons in the frogs and tendon counterparts called apodemes in the grasshoppers -- that store energy for their leaps. The difference, the science suggests, is the time they typically take before they take off.

"Our simulation is in line with the hypothesis that spring stiffness varies among organisms according to their jumps -- whether they are time-limited or non-time-limited," said Michael Rosario, a Brown University postdoctoral fellow and lead author of the study in the Proceedings of the Royal Society B.

Scientists already knew that the key spring in the grasshopper (the apodeme and part of its exoskeleton) has more than twice the stiffness as the analogous tendon in the bullfrog. By simulating the muscle-spring systems in each creature's legs, Rosario and his co-authors were able to show that the more time an animal has to contract muscle to store up energy before jumping, the more energy they can store in a relatively stiff spring.

Grasshoppers (Schistocerca gregaria) will normally spend 300 milliseconds storing up energy in their muscles, apodemes, and exoskeletons, although they have to jump more quickly, and perhaps less efficiently, to evade predators. Bullfrogs (Lithobates catesbeiana), on the other hand, normally spend only 50 milliseconds before making a leap, for instance to pounce toward prey. The simulations showed the greatest energy storage for a quick jump like that of the bullfrog was in a less stiff spring, while for the grasshopper's timeframe it was in a stiffer spring.

In other words, the creatures have the spring stiffness they should, given the time constraints on their typical jumping behavior.

"For both the bullfrog and the grasshopper, the time available for muscle contraction determined which spring stiffness permitted maximal energy storage," wrote Rosario and colleagues at Duke University (where he did most of the research before completing it at Brown), the University of Bristol, North Carolina State University and the University of North Carolina.

Rosario and his colleagues argue that the paper may help predict muscle and tendon properties for other organisms, including mammals. Further research, which Rosario is conducting in the lab of Brown University Professor Thomas Roberts, will determine whether that's too much of a leap.

In addition to Rosario, the paper's other authors are Gregory Sutton at Bristol, Sheila Patek at Duke and Gregory Sawicki in North Carolina.

Story Source:

Materials provided by Brown University. Note: Content may be edited for style and length.

Journal Reference:

M. V. Rosario, G. P. Sutton, S. N. Patek, G. S. Sawicki. Muscle–spring dynamics in time-limited, elastic movements. Proceedings of the Royal Society B: Biological Sciences, 2016; 283 (1838): 20161561 DOI: 10.1098/rspb.2016.1561  

Grasshoppers signal slow recovery of post-agricultural woodlands, study finds

Date:

November 24, 2014

Source:

University of Wisconsin-Madison

Summary:

By comparing grasshoppers found at woodland sites once used for agriculture to similar sites never disturbed by farming, researchers show that despite decades of recovery, the numbers and types of species found in each differ, as do the understory plants and other ecological variables, like soil properties.

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Grasshoppers are what they eat: New method to extract plant DNA from grasshopper guts sheds light on plant-insect interactions

Date:

February 5, 2014

Source:

American Journal of Botany

Summary:

Grasshoppers cause damage that costs landowners millions of dollars annually; however, grasshopper populations also play a positive role in cycling nutrients from decomposing plant matter back into the soil. A new method to recover high-quality DNA of ingested plant tissue from grasshopper guts can allow scientists to investigate their feeding patterns, and could help illuminate the impact of grasshoppers on plant communities.

Continued

Urban grasshoppers change their tune for females

Grasshoppers that live in noisy urban environments are having to change their song, a study has found.

Researchers suggest that high levels of background noise may affect the grasshoppers' mating process.

They say the insects are forced to increase the volume of the low-frequency sections of their call.

Results of the study, by scientists from the University of Bielefeld, Germany, are published in the journal Functional Ecology.

The research, which shows traffic noise could upset bow-winged grasshoppers' (Chorthippus biguttulus) mating system, is the first of its kind, according to lead researcher Ulrike Lampe.

"Effects of man-made noise on acoustic communication has only been studied with vertebrates, so far," said Ms Lampe, a PhD student at the University of Bielefeld's Department of Evolutionary Biology.

The scientists caught 188 male bow-winged grasshoppers from noisy roadsides and quiet rural locations.

Continued:  http://www.bbc.co.uk/nature/20310262

Unusual sighting - A pink grasshopper

August 2011. The rare grasshopper was spotted at Sandwich Bay Bird Observatory in Kent by Sue North. 
The Pink grasshopper is probably an unusual colour form of a common grasshopper - A few pink specimens are spotted every year - In fact this is the second one Wildlife Extra has been made aware of in the last few weeks.

They can be variable in colour with green, brownish, purple-red and pink forms recorded, although green forms are most common. Colour forms are genetically determined and some populations can show high frequency of pink grasshoppers.

Our thanks to Sue North for the image.
http://www.wildlifeextra.com/go/news/pink-grasshopper.html

The Worcestershire field filled with a million crickets

Five grasshoppers and crickets per square metre

August 2011: Wildlife experts estimate that at least 340kg of grasshoppers and crickets are living in one field of a Worcestershire nature reserve.

CRICKET GROUND: Roesel's bush crickets are among those that have been found in the nature reserve
Volunteers have counted an average of five grasshoppers and crickets per square metre in a field at Hill Court Farm nature reserve near Longdon in the south of the county. Based on this count, this one field alone, at more than 22 hectares in size, is home to over 1,136,500 grasshoppers and crickets.


Rob Allen, conservation officer for the Worcestershire Wildlife Trust which owns the nature reserve, said: ‘When we bought the reserve ten years ago the land was being used as an intensive dairy and arable farm. We've been working hard to recreate grazing marshes, wetlands and wildlife-friendly farmland.

‘Some of the species we're trying to encourage to return to the land are seriously affected by human disturbance so the nature reserve isn't generally open to the public.

‘We've recently had reports of many grassland insects on the reserve - some rarities as well as these fantastic numbers of grasshoppers and crickets.'

Some newcomers to the county
‘We think that an average grasshopper weighs around 300mg, crickets a little more. That equates to more than 340kg in just one field.'

Among the several species of grasshoppers and crickets found have been Roesel's bush cricket and long-winged coneheads. These are both relative newcomers to the county, having travelled north from the continent in the last couple of decades.


Another very new species to the county is Corizus hyoscyami. This red and black bug is usually found in sandy habitats of southern England but is now regularly being found inland, although few have been recorded in Worcestershire.

NEWCOMER: The Corizus hyoscyami

Rob continued: ‘We've also recently had a record of a six-belted clearwing moth. These scarce but attractive insects are associated with bird's-foot trefoil, one of their foodplants. The pupae live underground among the roots of the plant and need large areas of uncultivated flower-rich grassland.

‘The insect life found here is very promising for the future; a healthy insect population is part and parcel of a diverse ecosystem and well-functioning food-chain.'

Bright pink grasshopper spotted in Buckinghamshire

RIGHT: This bizarrely coloured grasshopper is believed to have a genetic mutation (Pic: Martin Rogers)

METRO REPORTER - 13th September, 2010

This bright pink grasshopper is enough to make anyone jump – and it wasn’t spotted in the jungles of Borneo or Brazil but in Buckinghamshire.

The 2.5cm (1in) insect was found in the Rushbed Woods nature reserve and its neon colouring is believed to stem from a genetic mutation in its reproductive cycle.

‘My daughter Nicola saw it first,’ said walker Martin Rogers.

‘She squealed, “Look, that flower is moving” as it jumped between the red flowers – presumably for camouflage.’

The sighting of the attractive-looking bug follows sightings of a similarly coloured insect at a Devon nature reserve.

Visitors to the reserve were taking part in a nature trail when they came across the pink lady (grasshopper).

Daniel Tate, 11-years-old at the time, said: 'I was really excited to hear that no one else had found a pink grasshopper at that place before.'

Fraser Rush, nature reserves officer for East Devon District Council, said: 'There are millions of common green grasshoppers but I have never seen a pink one.

'The female comes in a variety of colours, normally different shades of green and brown. Occasionally it tends towards purple, but this is a leap beyond that to pink.'

http://www.metro.co.uk/news/840731-bright-pink-grasshopper-spotted-in-buckinghamshire